Question

Express each of the following as the product of powers of their prime factors:

1. 648
2. 405

Answer 1

To express a number as the product of powers of their prime factors, we need to break down the number into its prime factors and then write them as a product.

Step-by-step explanation:

To express a number as the product of powers of their prime factors, we need to break down the number into its prime factors and then write them as a product. Let's take the examples provided:

1. To express 648 as the product of powers of its prime factors, we can break it down as follows:

648 = 2^4 * 3^4

So, 648 can be expressed as (2^4) * (3^4)

2. To express 405 as the product of powers of its prime factors, we can break it down as follows:

405 = 3^4 * 5^1

So, 405 can be expressed as (3^4) * (5^1)